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RE: Sum of 1/Primes

• To: mathgroup at smc.vnet.net
• Subject: [mg36973] RE: [mg36910] Sum of 1/Primes
• From: "DrBob" <drbob at bigfoot.com>
• Date: Thu, 3 Oct 2002 05:33:25 -0400 (EDT)
• Reply-to: <drbob at bigfoot.com>
• Sender: owner-wri-mathgroup at wolfram.com

No, Euler proved that series divergent in 1737.  It's the usual theorem
used to show that while the primes are sparse, they're not as sparse as
the squares (as the sum of THEIR inverses converges).

Bobby

-----Original Message-----
From: Matthias.Bode at oppenheim.de [mailto:Matthias.Bode at oppenheim.de] 
To: mathgroup at smc.vnet.net
Subject: [mg36973] [mg36910] Sum of 1/Primes

Dear Colleagues,

I calculated:

Sum[1/Prime[n], {n, 15000}] // N

Result: 2.74716

Now I wonder if this sum will converge or keep on growing, albeit very
slowly.

Best regards,

Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
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E-mail: matthias.bode at oppenheim.de
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